Rewrite as a logarithmic equation solver

Example 3: Solve the logarithmic equation This is an interesting problem. Study each case carefully before you start looking at the worked examples below.

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I think we are ready to set each argument equal to each other since we are able to reduce the problem to have a single log expression on each side of the equation.

Simplify the right side by the distributive property.

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But I have to express first the right side with the explicit denominator of 1. You do it by isolating the squared variable on one side and the constant on the other. These are your potential answers. Note that this is a Rational Equation.

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Move everything to one side, and that forces one side of the equation to be equal to zero. Step 2: By now you should know that when the base of the exponent and the base of the logarithm are the same, the left side can be written x. Therefore, exclude it as part of your solution. I think we are ready to set each argument equal to each other since we are able to reduce the problem to have a single log expression on each side of the equation. Notice that the expression inside the parenthesis stays on its current location, while the 5 becomes the exponent of the base. Solving for x, you should get these values as potential solutions. Drop the logs, set the arguments stuff inside the parenthesis equal to each other. After squaring both sides, it looks like we have a linear equation. If you have a single logarithm on one side of the equation then you can express it as an exponential equation and solve.

Here we see three log expressions and a constant. Solution: Step 1: Let both sides be exponents of the base e. Problem 1: Solve for x in the equation. Example 2: Solve the logarithmic equation Start by condensing the log expressions on the left into a single logarithm using the Product Rule.

So, we should disregard it as a solution.

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Logarithmic Form Calculator